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On the solvability of the Cauchy problem for a certain class of multidimensional loaded parabolic equations

I. V. Frolenkov^a, E. N. Kriger<sup>b

a</sup> Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk
^b JSC Information Satellite Systems Reshetnev, Zheleznogorsk, Krasnoyarsk Krai, Russia

Abstract: In this paper, we examine the solvability of a new class of nonclassical direct problems for multidimensional loaded parabolic equations with Cauchy data. We obtain sufficient conditions for the solvability of the problem; the proof is based on the method of weak approximation. By an example, we demonstrate the application of the theorem proved to the study of inverse problems for multidimensional parabolic equations with Cauchy data.

Keywords: parabolic equation, loaded equation, Cauchy problem, solvability, method of weak approximation.

UDC: 517.9

MSC: 35K15, 35B45, 35B65

 English version: Journal of Mathematical Sciences (New York), 2021, 254:6, 743–760

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